A propagation method self-consistent in the discrete domain for the simulation of large distance scenarios in a 3D inhomogeneous atmosphere is proposed. First, a spectral representation of the field in a discrete 3D domain over an infinite perfect ground is introduced in cylindrical coordinates. A discrete spectral propagator is then derived. As in 2D methods, the inhomogeneous atmosphere is considered in the spatial domain using phase screens. An explicit numerical scheme is introduced. For directive sources, a sectoral propagation is proposed to reduce the computation time by limiting the computation domain. The method is tested by simulation scenarios involving refractive effects in both vertical and azimuthal directions. The 3D refractive effects are shown to be properly simulated.